Gravitational energy-momentum pseudotensor in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> nonmetr
We derive the affine tensor associated with the energy and momentum densities of both gravitational and matter fields, the complex pseudo-tensor, for $f(Q)$ non-metric gravity, the straightforward extension of Symmetric Teleparallel Equivalent of General Relativity (STEGR), characterized by a flat, torsion-free, non-metric connection. The local conservation of energy-momentum complex on-shell is satisfied through a continuity equation. An important analogy is pointed out between gravitational pseudo-tensor of teleparallel $f(T)$ gravity, in the Weitzenböck gauge, and the same object of symmetric teleparallel $f(Q)$ gravity, in the coincident gauge. Furthermore, we perturb the gravitational pseudo-tensor $τ^α_{\phantomαλ}$ in the coincident gauge up to the second order in the metric perturbation, obtaining a useful expression for the power carried by the related gravitational waves. We also present an application of the gravitational pseudotensor, determining the gravitational energy density of a Schwarzschild spacetime in STEGR gravity, adopting the concident gauge. Finally, analyzing the conserved quantities on manifolds, the Stokes theorem can be formulated for generic affine connections
Authors
- Maurizio Capriolo (ORCID: https://orcid.org/0000-0003-1871-221X)
- Anonymous
- Gaetano Lambiase
Institutions
- University of Salerno (IT)
- Istituto Nazionale di Fisica Nucleare (IT)
- Scuola Superiore Meridionale (IT)
- University of Naples Federico II (IT)
Publication Details
- Journal
- Physical review. D/Physical review. D.
- Published
- 2026-01-15
- DOI
- https://doi.org/10.1103/1kvt-vvcf
- Primary Topic
- Cosmology and Gravitation Theories
- Type
- article
- Field-Weighted Citation Impact
- 0.00